Solve the inequality : 2x+3 =< 13
Given the inequality: 2x+3 =< 13
We need to find all possible x values that satisfies the inequality.
First we will need to isolate x on the left side.
==> 2x+3 =< 13
Subtract 3 from both sides.
==> 2x =< 10
Now we will divide by 2.
==> x =< 5
Then, the equality holds for all x values equal or less than 5.
==> x = ( -inf, 5]
We have to solve 2x + 3 <= 13
2x + 3 <= 13
=> 2x =< 13 - 3
=> 2x =< 10
=> x =< 5
The value of x lies in (-inf. , 5]
All we need to know is to determine the segment of the line that is below x axis. For this reason, we'll find out x values that makes the expression of the linear function to be negative:
2x + 3 - 13 =< 0
2x - 10 =< 0
2x =< 10
x =< 5
The values of x, for the segment of linear function is found below x axis, are located in the semi-closed interval (-infinite , 5].
The inequality 2x+3 =< 13 has to be solved.
If an equal term is added or subtracted from both the sides of an inequality, it is not altered.
2x+3 =< 13
Add -3 to both the sides.
2x+3-3 =< 13-3
2x <= 10
If the sides of an inequality are divided by a positive term it is not altered.
Divide the two sides of the inequality by 2
x <= 10/2
x <= 5
The solution of the inequality is all values of x less than or equal to 5.